Domain of Existence and Uniqueness for Nonlinear Hammerstein Integral Equations
| Autor: | Abhimanyu Kumar, Eulalia Martínez, Sukhjit Singh, Dikshi Gupta |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
hölder condition
Dynamical systems theory Iterative method General Mathematics Hammerstein integral equation Fréchet derivative 010103 numerical & computational mathematics 01 natural sciences Operator (computer programming) Holder condition Dynamical systems Computer Science (miscellaneous) Applied mathematics Uniqueness 0101 mathematics Engineering (miscellaneous) Mathematics lcsh:Mathematics lcsh:QA1-939 Lipschitz continuity Integral equation 010101 applied mathematics Nonlinear system Semilocal convergence Lipschitz condition MATEMATICA APLICADA |
| Zdroj: | Mathematics, Vol 8, Iss 3, p 384 (2020) RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia instname Mathematics Volume 8 Issue 3 |
| DOI: | 10.3390/math8030384 |
| Popis: | In this work, we performed an study about the domain of existence and uniqueness for an efficient fifth order iterative method for solving nonlinear problems treated in their infinite dimensional form. The hypotheses for the operator and starting guess are weaker than in the previous studies. We assume omega continuity condition on second order Fré chet derivative. This fact it is motivated by showing different problems where the nonlinear operators that define the equation do not verify Lipschitz and Hö lder condition however, these operators verify the omega condition established. Then, the semilocal convergence balls are obtained and the R-order of convergence and error bounds can be obtained by following thee main theorem. Finally, we perform a numerical experience by solving a nonlinear Hammerstein integral equations in order to show the applicability of the theoretical results by obtaining the existence and uniqueness balls. |
| Databáze: | OpenAIRE |
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